In the DVMP limit only the helicity non-flip amplitude \({\cal H}_{0-,++}^{P,tw3}\)  is left over
while \({\cal H}_{0-,-+}^{P,tw3}\)  vanishes \(\propto \hat{t}\)  as a
consequence of angular momentum conservation.
Thus, a full twist-3 DVMP analysis modifies the WW approximation
employed in [1]}, [2]} by a change of the DA \(\phi _{\pi p}\)  generated through the 3-body DA via the
equation of motion (REF ) and by the additional 3-body contributions.
From the properties of the 3-body DA, \(\phi _{3\pi }\) , ( see Eq. (REF )) it is clear that
the 3-body contributions Note that the 2-body twist-3 contribution proportional to \(\phi _{2\pi }^{EOM}\) 
and contributing to \({\cal H}^{P,qqg,C_F}\) 
vanishes for \(\hat{t}\rightarrow 0\) .
given in (REF )
do not have end-point singularities. On the other hand, the \(\phi _{\pi p}\)  contribution possesses
an end-point singularity since this DA does not vanish at the end points as we already remarked. This
singularity has been regularized in [1]}, [2]} by keeping the quark transverse momentum in the propagators.
More details on the twist-3 contribution in the DVMP limit will be given in a forthcoming paper [5]}.
